Convergence estimates of a semi-Lagrangian scheme for the ellipsoidal BGK model for polyatomic molecules

Abstract

In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the convection term with an implicit treatment for the relaxation term. We show how to explicitly solve the implicit step, thus obtaining an efficient and stable scheme for any Knudsen number. We also derive an explicit error estimate on the convergence of the proposed scheme for every fixed value of the Knudsen number.

BGK models for inert mixtures: comparison and applications

“…For the numerical solutions to BGK models, semi-Lagrangian methods proposed in [15,22] will be adopted together with a conservative reconstruction technique [12,13], which enables us to capture the correct behaviors of hydrodynamic limit models. As regards details and properties of semi-Lagrangian schemes (for single gas BGK model), we refer to papers regarding the construction of high order semi-Lagrangian schemes [8,20,33], treatment of boundary problems [21,32] and convergence analysis [9,34,35]. The paper is organized as follows.…”

“…where σ s =(10,13,16,9) and η s = (−30, −10, 10, 30), for s = 1, • • • , 4. We impose periodic boundary conditions on the space domain [−1, 1] and truncate velocity domain by[−15, 15].…”

A local velocity grid conservative semi-Lagrangian schemes for BGK model

“…Recently developed conservative semi-Lagrangian schemes allow accurate solutions on a wide range of Knudsen numbers, with very mild restrictions on the time step [9]. A related convergence proof of the SL scheme can be found in [3,16,17].…”